Problem: Justin runs at a constant rate, traveling $17 \text{ km}$ in $2$ hours. Write an equation that shows the relationship between $d$, the distance he runs in kilometers, and $h$, the time he spends running in hours.
Let's find the constant of proportionality. In the proportional relationship between $d$, the distance Justin runs in kilometers, and $h$, the time he spends running in hours, one constant of proportionality is his speed. It is the number we multiply by the time to get the distance. $h\,\times\, ?=d$ $\begin{aligned} h\,\times\, {?}&=d \\\\ {?}&=\dfrac{d}{h} \\\\ &=\dfrac{17}{2} \\\\ &={8.5} \end{aligned}$ The constant of proportionality is ${8.5}$. This means we can multiply ${8.5}$ by the time to get the distance. Now, let's write the equation: $\begin{aligned} \text{distance}&={\text{speed}}\times\text{time} \\\\ d&={8.5}h \end{aligned}$ One correct equation is: $d = 8.5h$